Today online networking has become an indispensable part of life for people all over the world. It is difficult for users to reduce their internet/online communications, as the flow of information increases everyday. While the free flow of information benefits online communications, the high toxicity of online communication is a drawback. Toxic texts are described as disrespectful or insulting messages that make the recipient feel uncomfortable. Deep Learning based Convolutional Neural Networks (CNN) have given exceptional outcomes in Computer Vision Domain, and AlexNet has proven to be the leading architecture in image classification and object detection problems. This article presents a 3-tier CNN architecture that is inspired by the AlexNet model to classify the toxic comments on the Wikipedia forum available in the Google Jigsaw dataset. Fast text-crawl-300d-2 m is used to formulate the pre-trained word embeddings matrix. The Exponential Linear Unit (ELU) activation function is applied in the Convolutional blocks for faster convergence. Dropout is used sufficiently along with different layers of the network to prevent overfitting. From the simulation and subsequent comparative analysis, it is found that the proposed model achieved a decent average accuracy of 98.505% and an average F1 score of 0.79. ROC-AUC score is used as an evaluation parameter. The value of ROC-AUC for the proposed model is approximately 0.9854, which shows that the said model differentiates between the comment classes more accurately.